The vertices of a triangle are P(-6,-4), Q(-6,-8) and R(2,-3). Name the vertices of the image reflected across the line y=x(1 point)

Answer 1

The line of reflection is the line y = x.
When reflecting a point across the line y = x, the x-coordinate and y-coordinate of the point switch places.
The vertices of the original triangle are P(-6,-4), Q(-6,-8), and R(2,-3).

When reflecting P(-6,-4) across the line y = x, the x-coordinate and y-coordinate switch places. So the reflected point is (-4, -6).
When reflecting Q(-6,-8) across the line y = x, the x-coordinate and y-coordinate switch places. So the reflected point is (-8, -6).
When reflecting R(2,-3) across the line y = x, the x-coordinate and y-coordinate switch places. So the reflected point is (-3, 2).

Therefore, the vertices of the image reflected across the line y = x are P'(-4, -6), Q'(-8, -6), and R'(-3, 2).

Answer 2

Find the image of O(-2,-1) after two reflections, first across the line y=-4 and then across the line x = 1(1 point)

Answer 3

To find the image of a point after two reflections, we need to reflect the point across one line first, and then reflect the resulting image across another line.

The point is O(-2, -1).

First, let's reflect O across the line y = -4.
- The y-coordinate of O remains the same.
- To find the new x-coordinate, we need to find the horizontal distance between O and the line y = -4, and then move the same distance on the other side of the line.
- The distance between O and the line y = -4 is 4 units.
- So, we move 4 units in the opposite direction to get the new x-coordinate.

The new x-coordinate is -2 - 4 = -6.
Therefore, the reflection of O(-2, -1) across the line y = -4 is O'(-6, -1).

Now, let's reflect O'(-6, -1) across the line x = 1.
- The x-coordinate of O' remains the same.
- To find the new y-coordinate, we need to find the vertical distance between O' and the line x = 1, and then move the same distance on the other side of the line.
- The distance between O' and the line x = 1 is |-6 - 1| = 7 units.
- So, we move 7 units in the opposite direction to get the new y-coordinate.

The new y-coordinate is -1 - 7 = -8.
Therefore, the reflection of O'(-6, -1) across the line x = 1 is O''(-6, -8).

So, the image of O(-2, -1) after two reflections, first across the line y = -4 and then across the line x = 1, is O''(-6, -8).